Mixtures of Skew-t Factor Analyzers

TL;DR

This paper introduces a novel mixture of skew-t factor analyzers for high-dimensional data clustering, offering flexible models and superior performance over Gaussian mixtures through an EM algorithm and BIC for model selection.

Contribution

It develops a new family of mixture models based on skew-t distributions, extending hyperbolic distribution mixtures, with flexible covariance constraints and an EM algorithm for estimation.

Findings

Superior clustering results on real and simulated data

Flexible models with eight covariance constraint variations

Effective model selection using BIC

Abstract

In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic distributions. Like their Gaussian and t-distribution analogues, our mixture of skew-t factor analyzers are very well-suited to the model-based clustering of high-dimensional data. Imposing constraints on components of the decomposed covariance parameter results in the development of eight flexible models. The alternating expectation-conditional maximization algorithm is used for model parameter estimation and the Bayesian information criterion is used for model selection. The models are applied to both real and simulated data, giving superior clustering results compared to a well-established family of Gaussian mixture models.